The grangolbit (or brangol[1])is equal to \(\underbrace{2^{...^{2^{100}}}}_{100\quad 2's}\)= 2^100#100 using Hyper-E notation.[2] The term was coined by Sbiis Saibian. It is equal to a power tower of 100 twos topped with 100.
Approximations in other notations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Arrow notation | \(22 \uparrow\uparrow 101\) | \(23 \uparrow\uparrow 101\) |
| Down-arrow notation | \(22 \downarrow\downarrow\downarrow 101\) | \(23 \downarrow\downarrow\downarrow 101\) |
| Steinhaus-Moser Notation | 99[4] | 100[4] |
| Chained arrow notation | \(22 \rightarrow 101 \rightarrow 2\) | \(23 \rightarrow 101 \rightarrow 2\) |
| BEAF | \(\{22,101,2\}\) | \(\{23,101,2\}\) |
| Hyperfactorial array notation | \(103!1\) | \(104!1\) |
| Bird's array notation | \(\{22,101,2\}\) | \(\{23,101,2\}\) |
| Strong array notation | \(s(22,101,2)\) | \(s(23,101,2)\) |
| Nested factorial notation | \(99![2]\) | \(100![2]\) |
| Fast-growing hierarchy | \(f_3(99)\) | \(f_3(100)\) |
| Hardy hierarchy | \(H_{\omega^3}(99)\) | \(H_{\omega^3}(100)\) |
| Slow-growing hierarchy | \(g_{\varepsilon_0}(100)\) | \(g_{\varepsilon_0}(101)\) |
Sources[]
- ↑ https://sites.google.com/site/largenumbers/home/appendix/a/ulnl2
- ↑ Saibian, Sbiis. 4.3.2 - Hyper-E Notation - Large Numbers. Retrieved 2016-07-18.